Hagel's prospective nomination -- which Obama is expected to make official Monday at 1:05 p.m. ET -- is "the worst possible message we could send to our friend Israel and the rest of our allies in the Middle East is Chuck Hagel," said Sen. John Cornyn, R-Texas.

Sen. Lindsey Graham, R-S.C., called the Hagel choice an "in-your-face nomination by the president."

And Senate Minority Leader Mitch McConnell, R-Ky., told ABC's This Week that "I'm going to wait and see how the hearings go and see whether Chuck's views square with the job he would be nominated to do."

Some gay rights groups have also come out against Hagel because of past comments for which the nominee has apologized. The Log Cabin Republicans took out a full page ad criticizing Hagel in Monday's Washington Post.

Hagel has also been critical of Israel's foreign policy, and once made a reference to the "Jewish lobby." He has suggested that Israel negotiate with Hamas, and the U.S. negotiate with Iran over its nuclear program. While he voted to authorize the 2003 invasion of Iraq, he later turned against the war and broke with some of his fellow Republicans.

Why would Obama, who had other options for the Pentagon slot, go with Hagel?

Sen. Dick Durbin, D-Ill., a key Obama ally in the Senate, told CNN's State of the Union that Obama won election, and "sitting back here and avoiding any confrontation and any controversy is going to make a weakened presidency."

Hagel's nomination did win initial support from Sen. Jack Reed, D-R.I., a member of the Armed Services Committee that will hold confirmation hearings.

Reed praised Hagel's "record of service to this country as a decorated combat veteran, successful CEO, senator, and statesman," and said that his "candor, judgment, and expertise will serve him well as our next Secretary of Defense."

Some Senate Democrats are more equivocal.

Sen. Ben Cardin, D-Md., told Current television he thinks Hagel would make a good secretary of Defense, but he needs some questions answered. Cardin called the prospective nomination "controversial," and, "we'll see how the confirmation process proceeds."

The Hagel story is contrast to that of Susan Rice.

Senate Republicans objected to the prospect of Rice, the United Nations ambassador, becoming secretary of State. Rice withdrew, and Obama went with Sen. John Kerry, R-Mass.

In an interview late last month, Obama told NBC's Meet The Press that his priority for Defense secretary "will be who's going to do the best job in helping to secure America."

As for Hagel, Obama noted that he served with him in the Senate.

"I know him," Obama said. "He is a patriot. He is somebody who has done extraordinary work both in the United States Senate, somebody who served this country with valor in Vietnam. And is somebody who's currently serving on my intelligence advisory board and doing an outstanding job."